In this paper an inventory routing problem is studied in which the goal is to determine an optimal distribution plan to replenish a set of customers by routing a limited fleet of capacitated vehicles over a discrete planning horizon. Each customer consumes a per period quantity of product and has a maximum inventory capacity. The goal is to minimize the total distribution cost that comprises the routing and the inventory holding costs. A matheuristic is presented, which uses the information gathered by a tabu search to build a sequence of mixed‐integer linear programming problems of small size. Extensive computational experiments are conducted on a large set of benchmark instances. The results show that the matheuristic outperforms other state‐of‐the‐art algorithms in terms of average solution quality.